Details

sample185.0ms

Algorithm

intervals

Results

79.0ms	1532×	body	80	nan
29.0ms	484×	body	80	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	32	10
1	65	10
2	181	8
3	522	8
4	2203	8
5	5002	8

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.7b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
0.7b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod`
10×	`pow1` `add-log-exp`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
3×	`times-frac` `exp-sum` `prod-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `associate-r/` `associate--l+` `clear-num` `sum-log` `flip--` `div-inv` `associate-/l/` `associate-/l`

Counts

4 → 95

Calls

4 calls:

7.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
10.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
7.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

series366.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (- t 1.0) (log a))
40.0ms	(* y (log z))
158.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
111.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

simplify52.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	493	869
1	2033	715
2	5001	683

prune331.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
0.3b	(* y (log (/ 1 z)))
0.3b	(* (log (/ 1 a)) t)
0.7b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
96×	`add-sqr-sqrt`
81×	`associate-r`
76×	`*-un-lft-identity`
75×	`add-cube-cbrt`
55×	`unpow-prod-down`
45×	`add-exp-log`
26×	`log-prod`
24×	`div-exp`
22×	`add-cbrt-cube`
17×	`exp-sum`
16×	`prod-exp`
14×	`pow1`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-l`
8×	`pow-exp` `div-inv` `unswap-sqr`
6×	`log-pow` `cbrt-unprod`
5×	`cbrt-undiv` `sqr-pow`
4×	`add-log-exp`
3×	`pow-prod-down` `associate-/r` `-commutative`
2×	`pow-to-exp` `rec-exp` `pow-flip` `1-exp` `associate-*r/` `log-rec` `inv-pow`
1×	`distribute-lft-neg-out` `frac-2neg` `clear-num` `distribute-rgt-neg-out` `associate-/l/` `associate-/l*`

Counts

4 → 199

Calls

4 calls:

28.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
6.0ms	(* y (log (/ 1 z)))
4.0ms	(* (log (/ 1 a)) t)
23.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

series776.0ms

Counts

4 → 12

Calls

4 calls:

335.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
37.0ms	(* y (log (/ 1 z)))
63.0ms	(* (log (/ 1 a)) t)
342.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify50.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1077	2667
1	5002	2322

prune818.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (/ 1 a)) t)
0.3b	(* (log (/ 1 a)) t)
0.3b	(* (log (/ 1 a)) t)
0.7b	(/ (* (* x (/ (pow (/ 1 (sqrt a)) 1.0) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) (/ (pow (/ 1 (sqrt a)) 1.0) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) y)

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

607×	`add-exp-log`
323×	`div-exp`
234×	`prod-exp`
112×	`pow-exp`
44×	`add-cbrt-cube`
28×	`pow-to-exp` `rec-exp` `1-exp`
19×	`cbrt-unprod`
18×	`add-sqr-sqrt` `associate-l`
17×	`cbrt-undiv`
16×	`pow1`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r` `log-pow`
4×	`add-log-exp`
3×	`distribute-lft-neg-out` `pow-flip` `times-frac` `associate-r/` `log-rec` `pow-prod-down` `associate-/r` `*-commutative` `associate-/l/` `inv-pow` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 194

Calls

4 calls:

5.0ms	(* (log (/ 1 a)) t)
5.0ms	(* (log (/ 1 a)) t)
5.0ms	(* (log (/ 1 a)) t)
62.0ms	(/ (* (* x (/ (pow (/ 1 (sqrt a)) 1.0) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) (/ (pow (/ 1 (sqrt a)) 1.0) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) y)

series775.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (log (/ 1 a)) t)
60.0ms	(* (log (/ 1 a)) t)
68.0ms	(* (log (/ 1 a)) t)
580.0ms	(/ (* (* x (/ (pow (/ 1 (sqrt a)) 1.0) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) (/ (pow (/ 1 (sqrt a)) 1.0) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) y)

simplify125.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	1245	5860
1	3649	5044
2	5001	4831

prune615.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (/ 1 a)) t)
0.3b	(* (log (/ 1 a)) t)
0.5b	(pow (/ 1 (sqrt a)) (* 2 1.0))
5.5b	(/ (/ y x) (/ (/ (pow (/ 1 (sqrt a)) (* 2 1.0)) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))

rewrite610.0ms

Algorithm

rewrite-expression-head

Rules

11987×	`times-frac`
3854×	`add-sqr-sqrt`
3850×	`add-cube-cbrt` `*-un-lft-identity`
2178×	`unpow-prod-down`
1680×	`cbrt-prod`
891×	`sqrt-prod`
427×	`div-inv`
420×	`exp-sum`
214×	`associate-/r*`
145×	`add-exp-log`
102×	`div-exp`
99×	`sqr-pow`
30×	`add-cbrt-cube`
22×	`cbrt-undiv`
20×	`pow-exp`
15×	`pow1`
14×	`prod-exp`
13×	`associate-/l*`
12×	`associate-l`
6×	`associate-r` `log-pow`
5×	`pow-to-exp` `rec-exp` `pow-flip` `pow-pow` `1-exp`
4×	`cbrt-unprod` `add-log-exp`
3×	`inv-pow`
2×	`distribute-lft-neg-out` `log-rec` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow-unpow` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/` `associate-/l/`

Counts

4 → 3142

Calls

4 calls:

5.0ms	(* (log (/ 1 a)) t)
5.0ms	(* (log (/ 1 a)) t)
7.0ms	(pow (/ 1 (sqrt a)) (* 2 1.0))
125.0ms	(/ (/ y x) (/ (/ (pow (/ 1 (sqrt a)) (* 2 1.0)) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))

series554.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (log (/ 1 a)) t)
64.0ms	(* (log (/ 1 a)) t)
124.0ms	(pow (/ 1 (sqrt a)) (* 2 1.0))
302.0ms	(/ (/ y x) (/ (/ (pow (/ 1 (sqrt a)) (* 2 1.0)) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))

simplify1.7s

Algorithm

egg-herbie

Counts

3154 → 3154

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5002	188951

prune20.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes198.0ms

Accuracy

0% (1.1b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 1.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	31	15

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.3s	44801×	body	80	nan
947.0ms	15051×	body	80	valid